Rewrite as a simplified fraction. ${0.81\overline{7} = {?}}$
Explanation: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 817.7777...\\ 100x &= 81.7777...\end{align*}}$ Subtracting the two equations, we have: ${900x = 736}$ ${x = \dfrac{736}{900}} $ ${x = \dfrac{184}{225}} $